The former Stuttgart manager said: "That was an unbelievable debut and this is just the start. He could become the player of the century."
In France, the headline in the dominant L'Equipe sports paper shouted simply: "Hip, Hip Rooney."
In Sweden, the Aftonbladet newspaper said: "It was the King's goal show."
Rooney will struggle to match Beckham's fame outside of football because of the Real Madrid player's showbiz lifestyle which is always going to attract attention.
But with United's popularity around the world - especially in Asia - Rooney has the potential to become a household name among sports fans across the globe in the next six months.